Equations, inequalities and graphs

On the axes, sketch the graph of $y = \frac{1}{3}(2x - 1)(x + 3)(2x + 5)$.

State the intercepts with the coordinate axes.

Solve the inequality $\frac{1}{3}(2x - 1)(x + 3)(2x + 5) > 0$.

On the axes, sketch the graph of $y = |x^2 - 5|$.
State the intercepts with the coordinate axes.

It is given that $\mathrm{f}(x) = ax + b$ where $a$ and $b$ are non-zero integers.
The solutions of the equation $|\mathrm{f}(x)| = 4$ are $x = 2.5$ and $x = -1.5$.

Find the possible expressions for $\mathrm{f}(x)$.

On the axes, sketch the graph of $y = |4x - 6|$, showing the points where the graph meets the axes.

Solve the equation $|4x - 6| = |2x|$.

On the axes, sketch the graph of $y = (2x - 5)(x + 3)(1 - x)$, stating the intercepts with the coordinate axes.

solve the inequality $(2x - 5)(x + 3)(1 - x) \leq 0$

on the axes below, sketch the graph of $y = |(2x - 5)(x + 3)(1 - x)|$.

On the axes, draw the graphs of $y = 5 + |3x - 2|$ and $y = 11 - x$.

Using the graphs, or otherwise, solve the inequality $11 - x < 5 + |3x - 2|$.